Final answer:
The car will skid 64 meters when it is traveling at 84 km/h as compared to skidding 16 meters at 42 km/h, due to the kinetic energy quadrupling when the speed is doubled.
Step-by-step explanation:
To determine the distance a car will skid with locked brakes at a higher speed, we can use the principles of physics related to kinetic energy and friction. When the brakes are applied, the kinetic energy of the car is converted into heat by the friction between the tires and the road surface. The work done by friction is equal to the kinetic energy the car had before it started to skid.
The kinetic energy (KE) of an object is given by the formula KE = ½ mv², where m is the mass of the object and v is its velocity. Assuming that the frictional force is constant, the distance d to stop a vehicle can be found by setting the work done by friction equal to the change in kinetic energy. Because the work done by friction is also equal to the frictional force times the distance (W = fd), and since kinetic energy is proportional to the square of the velocity, if a car's speed doubles, the kinetic energy will increase by a factor of four.
If a car skids 16 m when braking from 42 km/h, then when the speed is doubled to 84 km/h, the distance the car will skid will be 16 m multiplied by the square of the speed ratio (84/42)², which is 16 m multiplied by 4, equating to 64 m.